Mapping imprecise computation tasks on cyber-physical systems

Abstract

By allocating a set of tasks onto a set of nodes and adjusting the execution time of tasks, task mapping is an efficient approach to realize distributed computing. Cyber-Physical Systems (CPS), as a particular case of distributed systems, raise new challenges in task mapping, because of the heterogeneity and other properties traditionally associated with Wireless Sensor and Actuator Networks (WSAN), including shared sensing, acting and real-time computing. In addition, many of the real-time tasks of CPS can be executed in an imprecise way. Such systems accept an approximate result as long as the baseline Quality-of-Service (QoS) is satisfied and they can execute more computations to yield better results, if more system resources is available. These systems are typically considered under the Imprecise Computation (IC) model, achieving a better tradeoff between QoS and limited system resources. However, determining a QoS-aware mapping of these real-time IC-tasks onto the nodes of a CPS creates a set of interesting problems. In this paper, we firstly propose a mathematical model to capture the dependency, energy and real-time constraints of IC-tasks, as well as the sensing, acting, and routing in the CPS. The problem is formulated as a Mixed-Integer Non-Linear Programming (MINLP) due to the complex nature of the problem. Secondly, to efficiently solve this problem, we provide a linearization method that results in a Mixed-Integer Linear Programming (MILP) formulation of our original problem. Finally, we decompose the transformed problem into a task allocation subproblem and a task adjustment subproblem, and, then, we find the optimal solution based on subproblem iteration. Through the simulations, we demonstrate the effectiveness of the proposed method.